Higher Order Ambisonics denoted HOA offers one way of representing three-dimensional sound. Other techniques are wave field synthesis (WFS) or channel based methods like 22.2. In contrast to channel based methods, the HOA representation offers the advantage of being independent of a specific loudspeaker set-up. This flexibility, however, is at the expense of a decoding process which is required for the playback of the HOA representation on a particular loudspeaker set-up. Compared to the WFS approach where the number of required loudspeakers is usually very large, HOA may also be rendered to set-ups consisting of only few loudspeakers. A further advantage of HOA is that the same representation can also be employed without any modification for binaural rendering to head-phones.
HOA is based on a representation of the spatial density of complex harmonic plane wave amplitudes by a truncated Spherical Harmonics (SH) expansion. Each expansion coefficient is a function of angular frequency, which can be equivalently represented by a time domain function. Hence, without loss of generality, the complete HOA sound field representation actually can be assumed to consist of O time domain functions, where O denotes the number of expansion coefficients. These time domain functions will be equivalently referred to as HOA coefficient sequences in the following.
The spatial resolution of the HOA representation improves with a growing maximum order N of the expansion. Unfortunately, the number of expansion coefficients O grows quadratically with the order N, in particular O=(N+1)2. For example, typical HOA representations using order N=4 require O=25 HOA (expansion) coefficients. According to the above considerations, the total bit rate for the transmission of HOA representation, given a desired single-channel sampling rate fS and the number of bits Nb per sample, is determined by O·fS·Nb. Transmitting an HOA representation of order N=4 with a sampling rate of fS=48 kHz employing Nb=16 bits per sample will result in a bit rate of 19.2 MBits/s, which is very high for many practical applications, e.g. streaming. Therefore compression of HOA representations is highly desirable.